Abstract:
In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer *-semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer *-semigroups. © 2013 Polish Scientific Publishers.
Registro:
Documento: |
Artículo
|
Título: | Two-valued states on Baer *-semigroups |
Autor: | Freytes, H.; Domenech, G.; De Ronde, C. |
Filiación: | Instituto Argentino de Matemática (IAM), Saavedra 15, 3er piso, 1083 Buenos Aires, Argentina Dipartimento di Matematica e Informatica U. Dini, Viale Morgagni 67/a, 50134 Firenze, Italy Instituto de Astronomía y Física del Espacio (IAFE), Casilla de Correo 67, Sucursal 28, 1428 Buenos Aires, Argentina Instituto de Filosofía Dr. Alejandro Korn. (UBA-CONICET), Buenos Aires, Argentina Center Leo Apostel (CLEA) and Foundations of the Exact Sciences (FUND), Brussels Free University, Krijgskundestraat 33, 1160 Brussels, Belgium
|
Palabras clave: | 02.10 De; Orthomodular lattices; Two-valued states |
Año: | 2013
|
Volumen: | 72
|
Número: | 3
|
Página de inicio: | 287
|
Página de fin: | 310
|
DOI: |
http://dx.doi.org/10.1016/S0034-4877(14)60019-7 |
Título revista: | Reports on Mathematical Physics
|
Título revista abreviado: | Rep. Math. Phys.
|
ISSN: | 00344877
|
CODEN: | RMHPB
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00344877_v72_n3_p287_Freytes |
Referencias:
- Adams, D., Equational classes of Foulis semigroups and orthomodular lattices (1973) Proc. Univ. of Houston, Lattice Theory Conf., pp. 486-497. , Houston
- Birkhoff, G., Von Neumann, J., The logic of quantum mechanics (1936) Ann. Math., 27, pp. 823-843
- Blyth, T.S., Janowitz, M.F., (1972) Residuation Theory, , Pergamon Press
- Burris, S., Sankappanavar, H.P., (1981) A Course in Universal Algebra, Graduate Text in Mathematics Vol. 78, , SpringerVerlag, New York Heidelberg Berlin
- Domenech, G., Freytes, H., de Ronde, C., Equational characterization for two-valued states in orthomodular quantum systems (2011) Rep. Math. Phys., 68, pp. 65-83
- Dalla Chiara, M.L., Giuntini, R., Greechie, R., (2004) Reasoning in Quantum Theory, Sharp and Unsharp Quantum Logics, , Kluwer, Dordrecht-Boston-London
- Dvurečenskij, A., On States on MV-algebras and their applications (2011) J. Logic Computation, 21 (3), pp. 407-427
- Foulis, D., Baer *-semigroups (1960) Procc. American Math. Soc., 11, pp. 648-654
- Foulis, D., Observables, states, and symmetries in the context of C B-effect algebras (2007) Rep. Math. Phys., 60, pp. 329-346
- Gleason, A.M., Measures on the closed subspaces of a Hilbert space (1957) J. Math. Mech., 6, pp. 885-893
- Gudder, S., (1979) Stochastic Methods in Quantum Mechanics, , Elseiver-North-Holand, New York
- Jauch, J., (1968) Foundations of Quantum Mechanics, , Addison Wesley, Reading, Mass
- Kalman, J.A., Lattices with involution (1958) Trans. Amer. Math. Soc., 87, pp. 485-491
- Kalmbach, G., (1983) Ortomodular Lattices, , Academic Press, London
- Kühr, J., Mundici, D., De Finetti theorem and Borel states in [0, 1]-valued logic (2007) Int J. Approx. Reason, 46 (3), pp. 605-616
- Kroupa, T., Every state on semisimple MV-algebra is integral (2006) Fuzzy Sets Syst., 157, pp. 2771-2787
- Harding, J., Pták, P., On the set representation of an orthomodular poset (2001) Colloquium Math., 89, pp. 233-240
- Mackey, G.W., (1963) Mathematical Foundations of Quantum Mechanics, , W. A. Benjamin, New York
- Messiah, A., Quantum Mechanics (1961), 1. , North-Holand Publishing Company, Amsterdan; Maeda, F., Maeda, S., (1970) Theory of Symmetric Lattices, , Springer, Berlin
- Navara, M., Descriptions of state spaces of orthomodular lattices (1992) Math. Bohemica, 117, pp. 305-313
- Navara, M., Triangular norms and measure of fuzzy set (2005) Logical, Algebraic, Analytic and Probabilistic Aspect of Triangular Norms, pp. 345-390. , Elsevier, Amsterdam
- Von Neumann, J., Mathematical Foundations of Quantum Mechanics (1996), Princeton University Press, 12th. edition, Princeton; Piron, C., (1976) Foundations of Quantum Physics, , Benjamin, Reading, Mass
- Pool, J.C., Baer *-semigroups and the logic of quantum mechanics (1968) Commun. Math. Phys., 9, pp. 118-141
- Pták, P., Pulmannová, S., (1991) Orthomodular Structures as Quantum Logics, , Kluwer, Dordrecht
- Pulmannová, S., Sharp and unsharp observables on s-MV algebras. a comparison with the Hilbert space approach (2008) Fuzzy Sets Syst., 159 (22), pp. 3065-3077
- Pták, P., Weak dispersion-free states and hidden variables hypothesis (1983) J. Math. Phys., 24, pp. 839-840
- Riečanová, Z., Continuous lattice effect algebras admitting order-continuous states (2003) Fuzzy Sets Syst., 136, pp. 41-54
- Riečanová, Z., Effect algebraic extensions of generalized effect algebras and two-valued states (2008) Fuzzy Sets Syst., 159, pp. 1116-1122
- Rüttimann, G.T., Jauch-Piron states (1977) J. Math. Phys., 18, pp. 189-193
- Tkadlec, J., Partially additive measures and set representation of orthoposets (1993) J. Pure Appl. Algebra, 86, pp. 79-94
- Tkadlec, J., Partially additive states on orthomodular posets (1995) Colloquium Mathematicum, LXII, pp. 7-14
- Tkadlec, J., Boolean orthoposets and two-valued states on them (1992) Rep. Math. Phys., 31, pp. 311-316
Citas:
---------- APA ----------
Freytes, H., Domenech, G. & De Ronde, C.
(2013)
. Two-valued states on Baer *-semigroups. Reports on Mathematical Physics, 72(3), 287-310.
http://dx.doi.org/10.1016/S0034-4877(14)60019-7---------- CHICAGO ----------
Freytes, H., Domenech, G., De Ronde, C.
"Two-valued states on Baer *-semigroups"
. Reports on Mathematical Physics 72, no. 3
(2013) : 287-310.
http://dx.doi.org/10.1016/S0034-4877(14)60019-7---------- MLA ----------
Freytes, H., Domenech, G., De Ronde, C.
"Two-valued states on Baer *-semigroups"
. Reports on Mathematical Physics, vol. 72, no. 3, 2013, pp. 287-310.
http://dx.doi.org/10.1016/S0034-4877(14)60019-7---------- VANCOUVER ----------
Freytes, H., Domenech, G., De Ronde, C. Two-valued states on Baer *-semigroups. Rep. Math. Phys. 2013;72(3):287-310.
http://dx.doi.org/10.1016/S0034-4877(14)60019-7